Anyon collision experiments have recently demonstrated the ability to discriminate between fermionic and anyonic statistics. However, only one type of anyons associated with the simple Laughlin state at filling factor $\nu =1/3$ has been probed so far. It is now important to establish anyon collisions as quantitative probes of fractional statistics for more complex topological orders, with the ability to distinguish between different species of anyons with different statistics. In this work, we use the anyon collider to compare the Laughlin $\nu =1/3$ state, which is used as the reference state, with the more complex Jain state at $\nu =2/5$, where low energy excitations are carried by two copropagating edge channels. We demonstrate that anyons generated on the outer channel of the $\nu =2/5$ state (with a fractional charge $e^{*}=e/3$) have a similar behavior compared to $\nu =1/3$, showing the robustness of anyon collision signals for anyons of the same type. In contrast, anyons emitted on the inner channel of $\nu =2/5$ (with a fractional charge $e^{*}=e/5$) exhibit a reduced degree of bunching compared to the $\nu =1/3$ case, demonstrating the ability of the anyon collider to discriminate not only between anyons and fermions, but also between different species of anyons associated with different topological orders of the bulk. Our experimental results for the inner channel of $\nu =2/5$ also point toward an influence of interchannel interactions in anyon collision experiments when several copropagating edge channels are present. A quantitative understanding of these effects will be important for extensions of anyon collisions to non-Abelian topological orders, where several charged and neutral modes propagate at the edge.